Three consecutive integers
The correct answer and explanation is:
To find three consecutive integers, we need to use algebraic expressions. Let the three consecutive integers be represented by the variable xx, where xx is the first integer. The next two consecutive integers can be written as x+1x+1 and x+2x+2.
For example, if the first integer is 5, then the three consecutive integers are:
- First integer: 55
- Second integer: 5+1=65 + 1 = 6
- Third integer: 5+2=75 + 2 = 7
These integers are consecutive because each one is exactly one more than the previous one.
Steps:
- Assign a variable xx to represent the first integer.
- Write the next two consecutive integers as x+1x+1 and x+2x+2.
- You can now use these expressions to solve for unknowns when given additional information, such as the sum or product of the integers.
For example, if you are given that the sum of the three integers is 42, you can write the equation: x+(x+1)+(x+2)=42x + (x + 1) + (x + 2) = 42
Simplify the equation: 3x+3=423x + 3 = 42
Now, subtract 3 from both sides: 3x=393x = 39
Then, divide by 3: x=13x = 13
Thus, the three consecutive integers are 1313, 1414, and 1515.
This process can be applied to any scenario involving three consecutive integers. The general method is to represent the integers algebraically and use additional information, like their sum or product, to solve for xx.